消除左递归
1.将以下文法消除左递归，分析符号串 i*i+i 。
并分别求FIRST集、FOLLOW集，和SELECT集
E -> E+T | T
T -> T*F | F
F -> (E) | i
答：消除左递归：
E -> TE'
E' -> +TE' | ɛ
T -> FT'
T' -> *FT' | ɛ
F -> (E) | i
分析符号串：
FIRST集：
FIRST(E) = { ( , i }
FIRST(E') = { + , ɛ }
FIRST(T) = { ( , i }
FIRST(T') = { * , ɛ }
FIRST(F) = { ( , i }
FOLLOW集：
FOLLOW(E) = { ) , # }
FOLLOW(E') = { ) , # }
FOLLOW(T) = { + , ) , # }
FOLLOW(T') = { + , ) , # }
FOLLOW(F) = { * , + , ) , # }
SELECT集：
SELECT(E -> TE') = { ( , i }
SELECT(E' -> +TE') = { + }
SELECT(E' -> ɛ) = { ) , # }
SELECT(T -> FT') = { ( , i }
SELECT(T' -> *FT' ) ={ * }
SELECT(T' -> ɛ) = { + , ) , # }
SELECT(F -> (E) ) = { ( , i }
SELECT(F -> i ) = { i }
2.P101练习7（2）（3）文法改写，并分别求FIRST集、FOLLOW集，和SELECT集
（2）
S->Ap
A->a |ε
A->cA
A->aA
答：
对A提取公共左因子：
A -> aC
C -> ABe | ɛ
B -> dB'
B' -> bB' | ɛ
FIRST集：
FIRST(A) = { a }
FIRST(C) = { ABe , ɛ } = { e , ɛ }
FIRST(ɛ) = { ɛ }
FIRST(dB’) = { d }
FIRST(bB') = { b }
FOLLOW集：
FOLLOW(A) = { d , # }
FOLLOW(C) = { d , # }
FOLLOW(B) = { e }
FOLLOW(B') = { e }
SELECT集：
SELECT(A -> aC) = { a }
SELECT(C -> ABe) = { a}
SELECT(C -> ɛ) = { d , # }
SELECT(B -> dB') = { d }
SELECT(B' -> bB') ={ b }
SELECT(B' -> ɛ) ={ e }
（3）S->Aa | b
A->SB
B->ab
答：
文法改写：
S->bS'
S'->BaS' | ε
B->ab
FIRST集：
FIRST(bS’) = { b }
FIRST(BaS') = { a }
FIRST(ɛ) = { ɛ }
FIRST(ab) = { a }
FOLLOW集：
FOLLOW(S) = { # }
FOLLOW(S') = { # }
FOLLOW(B) = { b }
SELECT集：
SELECT(S -> bS') = { b }
SELECT(S' -> BaS' ) = { a }
SELECT(S' -> ɛ) = { # }
SELECT(B -> ab) = { a }
课堂练习：
求以下文法的FIRST集、FOLLOW集和SELECT集。
S->Ap
A->a |ε
A->cA
A->aA
答：
FIRST集：
FIRST(Ap) = { a , c , p }
FIRST(a) = { a }
FIRST(ɛ) = { ɛ }
FIRST(cA) = { c }
FIRST(aA) = { a }
FOLLOW集：
FOLLOW(S) = { # }
FOLLOW(A) = { p }
SELECT集：
SELECT(S -> Ap) = { a , c , p }
SELECT(A -> a ) = { a }
SELECT(A -> ɛ) = { p }
SELECT(A -> cA) = { c }
SELECT(A -> Aa) ={ a }
（2）
S->Ap
S->Bq
A->a
A->cA
B->b
B->dB
答：
FIRST集：
FIRST(S1) = FIRST(Ap) = { a , c }
FIRST(S2) = FIRST(Bq) = { b , d }
FIRST(a) = { a }
FIRST(cA) = { c }
FIRST(b) = { b }
FIRST(dB) = { d }
FOLLOW集：
FOLLOW(S) = { # }
FOLLOW(A) = { p }
FOLLOW(B) = { q }
SELECT集：
SELECT(S -> Ap) = { a , c }
SELECT(S -> Bq ) = { b , d }
SELECT(A -> a) = { a }
SELECT(A -> cA) = { c }
SELECT(B -> b) ={ b }
SELECT(B -> dB) ={ d }
